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CRANK–NICOLSON ALTERNATIVE DIRECTION IMPLICIT METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NONSEPARABLE COEFFICIENTS
XUE-LEI LIN1; MICHAEL K. NG1; HAI-WEI SUN2
2019-05-07
Source PublicationSIAM Journal on Numerical Analysis
ISSN0036-1429
Volume57Issue:3Pages:997-1019
Abstract

In this paper, we study the Crank–Nicolson alternative direction implicit (ADI) method for two-dimensional Riesz space-fractional diffusion equations with nonseparable coefficients. Existing ADI methods are only shown to be unconditional stable when coefficients are some special separable functions. The main contribution of this paper is to show under mild assumptions the unconditional stability of the proposed Crank–Nicolson ADI method in discrete norm and the consistency of cross perturbation terms arising from the Crank–Nicolson ADI method. Also, we demonstrate that several consistent spatial discretization schemes satisfy the required assumptions. Numerical results are presented to examine the accuracy and the efficiency of the proposed ADI methods.

KeywordNonseparable Variable Coefficients Crank–nicolson Adi Methods Space-fractional Diffusion Equations Unconditional Stability Analysis
DOIhttps://doi.org/10.1137/18M1195693
Indexed BySCI
Language英语
WOS Research AreaMathematics
WOS SubjectMathematics, Applied
WOS IDWOS:000473085400002
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Document TypeJournal article
CollectionFaculty of Science and Technology
DEPARTMENT OF MATHEMATICS
Corresponding AuthorMICHAEL K. NG
Affiliation1.Department of Mathematics, Hong Kong Baptist University, Kowloon Tong, Hong Kong
2.Department of Mathematics, University of Macau, Macau, Macau
Recommended Citation
GB/T 7714
XUE-LEI LIN,MICHAEL K. NG,HAI-WEI SUN. CRANK–NICOLSON ALTERNATIVE DIRECTION IMPLICIT METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NONSEPARABLE COEFFICIENTS[J]. SIAM Journal on Numerical Analysis,2019,57(3):997-1019.
APA XUE-LEI LIN,MICHAEL K. NG,&HAI-WEI SUN.(2019).CRANK–NICOLSON ALTERNATIVE DIRECTION IMPLICIT METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NONSEPARABLE COEFFICIENTS.SIAM Journal on Numerical Analysis,57(3),997-1019.
MLA XUE-LEI LIN,et al."CRANK–NICOLSON ALTERNATIVE DIRECTION IMPLICIT METHOD FOR SPACE-FRACTIONAL DIFFUSION EQUATIONS WITH NONSEPARABLE COEFFICIENTS".SIAM Journal on Numerical Analysis 57.3(2019):997-1019.
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